A188888 - OEIS

%I #30 Aug 09 2024 01:53:09

%S 1,1,13,1,2,15,10,1,18,1,1,21,2,1,1,2,4,5,2,2,2,11,1,2,2,3,1,1,10,1,2,

%T 1,2,3,2,3,15,1,2,3,1,1,90,1,44,2,4,10,1,11,9,1,17,1,8,2,2,6,2,6,1,3,

%U 1,1,1,2,20,1,7,27,1,19,40,1,304,1,1,2,1,1,1,62,1,1,2,1,2,1,32,1,1,1,11,1,20,1,85,1,1,1,3,3,13,1,4,1,3,1,3,1,16,1,9,3,2,1,1,30,2,1

%N Continued fraction of sqrt(2 + sqrt(3)) or 2*cos(Pi/12).

%C For a geometric interpretation, see A188640 and A188887.

%H G. C. Greubel, <a href="/A188888/b188888.txt">Table of n, a(n) for n = 0..9999</a>

%e sqrt(2+sqrt(3)) = [1,1,13,1,2,15,10,1,18,1,1,21,2,1,1,2,4,...].

%p with(numtheory): cfrac(sqrt(2+sqrt(3)),120,'quotients'); # _Muniru A Asiru_, Sep 30 2018

%t r = 2^(1/2); t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t]

%t N[t, 130]

%t RealDigits[N[t, 130]][[1]]

%t ContinuedFraction[t, 120]

%t ContinuedFraction[Sqrt[2+Sqrt[3]],120] (* _Harvey P. Dale_, Jul 19 2014 *)

%o (PARI) default(realprecision, 100); contfrac(sqrt(2 + sqrt(3))) \\ _G. C. Greubel_, Sep 29 2018

%o (Magma) SetDefaultRealField(RealField(100));  ContinuedFraction(Sqrt(2 + Sqrt(3))); // _G. C. Greubel_, Sep 29 2018

%Y Cf. A188887 (decimal expansion).

%K nonn,cofr

%O 0,3

%A _Clark Kimberling_, Apr 12 2011

%E Name extended by _Greg Dresden_, Apr 13 2018

%E Offset changed by _Andrew Howroyd_, Aug 08 2024